CHEM 140LSession 3 - Data Analysis in Excel3-2Basic Statistics in ScienceExperimental measurements always have some sort of error. This means no conclusioncan be made with complete certainty. Statistics provide the tools to accept experimentalresults that have a high probability of being correct or to reject experimental results thatfall beyond acceptable confidence limits. This session will address the basic statisticsused in science.=DistributionsConsider the example, that a food manufacturer claims that there are 100 mg of sodium ina can of soup. Five cans of soup were tested and it was found that the sodium contentwas 108.6 mg, 104.2 mg, 96.1 mg, 99.6 mg and 102.2 mg. Each can of soup is known asa sample. As we can see no individual sample contains the exact sodium contentreported by the manufacturer, but all the values are close to 100 mg. The discrepancybetween the sodium content of an individual sample and the reported sodium content isdue to some degree of random error or fluctuation in the system.If the measurements were repeated enough times, we would expect a spread of results ora distributionof the values. The distribution of a few measurements would look like theplot shown in Figure 3.2. The frequency is the number of times that a particular resultsoccurs.Figure 3.1: Population versus sample.

CHEM 140LSession 3 - Data Analysis in Excel3-3With the example shown in Figure 3.2, we see that the values are distributed relativelyevenly around a point somewhere between 1.2 and 1.6. You can see the probabilitydistribution plot has a “bell shape”. This type of distribution is known as a bell-curveor normal distribution. A normal distribution implies that a large number of measurementswere made for the same system.=MeanAs you can see from Figure 3.3, as we increase the number of measurements, the shapeof the probability plot begins to resemble the normal distribution. The mean (or average)of a set of measurements is located at the centre of the normal distribution. The meancan be thought of as the expected outcome of an event, such that if a measurement wasperformed multiple times, the average values would be the most common outcome. If aninfinite number of measurements are made, the average of the infinite measurements isknown as the population mean(μ). The population means represents the “true” value ofa measurement. Since it is impossible to measure directly a population mean, normally a

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